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Evidence for F-Theory

We construct compact examples of D-manifolds for type IIB strings. The construction has a natural interpretation in terms of compactification of a 12 dimensional F-theory'. We provide evidence for a more natural reformulation of type IIB theory in terms of F-theory. Compactification of M-theory on a manifold $K$ which admits elliptic fibration is equivalent to compactification of F-theory on $K\times S^1$. A large class of $N=1$ theories in 6 dimensions are obtained by compactification of F-theory on Calabi-Yau threefolds. A class of phenomenologically promising compactifications of F-theory is on $Spin(7)$ holonomy manifolds down to 4 dimensions. This may provide a concrete realization of Witten's proposal for solving the cosmological constant problem in four dimensions.

F-Theory, T-Duality on K3 Surfaces and N=2 Supersymmetric Gauge Theories in Four Dimensions

We construct T-duality on K3 surfaces. The T-duality exchanges a 4-brane R-R charge and a 0-brane R-R charge. We study the action of the T-duality on the moduli space of 0-branes located at points of K3 and 4-branes wrapping it. We apply the construction to F-theory compactified on a Calabi-Yau 4-fold and study the duality of N=2 SU(N_c) gauge theories in four dimensions. We discuss the generalization to the N=1 duality scenario.

Towards a Field Theory of F-theory[3]

We make a proposal for a bosonic field theory in twelve dimensions that admits the bosonic sector of eleven-dimensional supergravity as a consistent truncation.

It can also be consistently truncated to a ten-dimensional Lagrangian that contains all the BPS p-brane solitons of the type IIB theory. The mechanism allowing the consistent truncation in the latter case is unusual, in that additional fields with an off-diagonal kinetic term are non-vanishing and yet do not contribute to the dynamics of the ten-dimensional theory. They do, however, influence the oxidation of solutions back to twelve dimensions.

We present a discussion of the oxidations of all the basic BPS solitons of M-theory and the type IIB string to D=12. In particular, the NS-NS and R-R strings of the type IIB theory arise as the wrappings of membranes in D=12 around one or other circle of the compactifying 2-torus.

Stringy Cosmic Strings and Compactifications of F-theory

We construct stringy cosmic string solutions corresponding to compactifications of F-theory on several elliptic Calabi-Yau manifolds by solving the equations of motion of low energy effective action of ten dimensional type IIB superstring theory. Existence of such solutions supports the compactifications of F-theory.

F-Theory and the universal string theory

We apply the techniques of the universal string theory'' to the manifold'' paradigm for superstring/M-theory and come up with a candidate manifold: the manifold of F-theory vacua, defined in conformal field theoretical terms. It contains the five known superstring theories as particular vacua; although the natural vacua are (10+2)-dimensional. As a byproduct, a natural explanation emerges for the compactness of the extra two coordinates in F-theory.

From M-theory to F-theory, with Branes

A duality relationship between certain brane configurations in type IIA and type IIB string theory is explored by exploiting the geometrical origins of each theory in M-theory. The configurations are dual ways of realising the non-perturbative dynamics of a four dimensional N=2 supersymmetric SU(2) gauge theory with four or fewer favours of fermions in the fundamental, and the spectral curve which organizes these dynamics plays a prominent role in each case. This is an illustration of how non-trivial F-theory backgrounds follow from M-theory ones, hopefully demystifying somewhat the origins of the former.

M-Theory Versus F-Theory Pictures of the Heterotic String

If one begins with the assertion that the type IIA string compactified on a K3 surface is equivalent to the heterotic string on a four-torus one may try to find a statement about duality in ten dimensions by decompactifying the four-torus. Such a decompactification renders the K3 surface highly singular. The resultant K3 surface may be analyzed in two quite different ways - one of which is natural from the point of view of differential geometry and the other from the point of view of algebraic geometry. We see how the former leads to a "squashed K3 surface" and reproduces the Horava-Witten picture of the heterotic string in M-theory. The latter produces a "stable degeneration" and is tied more closely to F-theory. We use the relationship between these degenerations to obtain the M-theory picture of a point-like E8-instanton directly from the F-theory picture of the same object.

Orientifold Limit of F-theory Vacua

We show how F-theory on a Calabi-Yau (n+1)-fold, in appropriate limit, can be identified as an orientifold of type IIB string theory compactified on a Calabi-Yau n-fold.

An approach to F-theory

We consider BPS configurations in theories with two timelike directions from the perspective of the supersymmetry algebra. We show that whereas a BPS state in a theory with one timelike variable must have positive energy, in a theory with two times any BPS state must have positive angular momentum in the timelike plane, in that $Z_{0\tilde{0}}>0$, where $0$ and $\tilde{0}$ are the two timelike directions. We consider some generic BPS solutions of theories with two timelike directions, and then specialise to the study of the (10,2) dimensional superalgebra for which the spinor operators generate 2-forms and 6-forms. We argue that the BPS configurations of this algebra relate to F-theory in the same way that the BPS configurations of the eleven dimensional supersymmetry algebra relate to M-theory. We show that the twelve dimensional theory is one of fundamental 3-branes and 7-branes, along with their dual partners. We then formulate the new intersection rules for these objects. Upon reduction of this system we find the algebraic description of the IIB-branes and the M-branes. Given these correspondences we may begin an algebraic study of F-theory.

F-theory and linear sigma models

We present an explicit method for translating between the linear sigma model and the spectral cover description of SU(r) stable bundles over an elliptically fibered Calabi-Yau manifold. We use this to investigate the 4-dimensional duality between (0,2) heterotic and F-theory compactifications. We indirectly find that much interesting heterotic information must be contained in the spectral bundle' and in its dual description as a gauge theory on multiple F-theory 7-branes.

A by-product of these efforts is a method for analyzing semistability and the splitting type of vector bundles over an elliptic curve given as the sheaf cohomology of a monad.

Non-transversal colliding singularities in F-theory

This is a short introduction to the study of compactifications of F-theory on elliptic Calabi-Yau threefolds near colliding singularities. In particular we consider the case of non-transversal intersections of the singular fibers.

ICMP lecture on Heterotic/F-theory duality

The heterotic string compactified on an (n-1)-dimensional elliptically fibered Calabi-Yau Z-->B is conjectured to be dual to F-theory compactified on an n-dimensional Calabi-Yau X-->B, fibered over the same base with elliptic K3 fibers. In particular, the moduli of the two theories should be isomorphic. The cases most relevant to the physics are n=2, 3, 4, i.e. the compactification is to dimensions d=8, 6 or 4 respectively. Mathematically, the richest picture seems to emerge for n=3, where the moduli space involves an analytically integrable system whose fibers admit rather different descriptions in the two theories. The purpose of this talk is to review some of what is known and what is not yet known about this conjectural isomorphism. Some of the underlying mathematics of principal bundles on elliptic fibrations is reviewed in the accompanying Taniguchi talk (hep-th/9802094).

On the Complementarity of F-theory, Orientifolds, and Heterotic Strings

We study F-theory duals of six dimensional heterotic vacua in extreme regions of moduli space where the heterotic string is very strongly coupled. We demonstrate how to use orientifold limits of these F-theory duals to regain a perturbative string description. As an example, we reproduce the spectrum of a $T^4/\ZZ_{4}$ orientifold as an F-theory vacuum with a singular $K3$ fibration. We relate this vacuum to previously studied heterotic $E_8\times E_8$ compactifications on $K3$.

Compactifications of F-Theory on Calabi-Yau Fourfolds [14]

The enhanced gauge groups in F-theory compactified on elliptic Calabi-Yau fourfolds are investigated in terms of toric geometry.

Type IIB Orientifolds, F-theory, Type I Strings on Orbifolds and Type I - Heterotic Duality

We consider six and four dimensional ${\cal N}=1$ supersymmetric orientifolds of Type IIB compactified on orbifolds. We give the conditions under which the perturbative world-sheet orientifold approach is adequate, and list the four dimensional ${\cal N}=1$ orientifolds (which are rather constrained) that satisfy these conditions. We argue that in most cases orientifolds contain non-perturbative sectors that are missing in the world-sheet approach. These non-perturbative sectors can be thought of as arising from D-branes wrapping various collapsed 2-cycles in the orbifold. Using these observations, we explain certain puzzles'' in the literature on four dimensional orientifolds. In particular, in some four dimensional orientifolds the naive'' tadpole cancellation conditions have no solution. However, these tadpole cancellation conditions are derived using the world-sheet approach which we argue to be inadequate in these cases due to appearance of additional non-perturbative sectors. The main tools in our analyses are the map between F-theory and orientifold vacua and Type I-heterotic duality. Utilizing the consistency conditions we have found in this paper, we discuss consistent four dimensional chiral ${\cal N}=1$ Type I vacua which are non-perturbative from the heterotic viewpoint.

Matter in F-Theory

It is shown that the matter content of F-theory compactifications on elliptic Calabi-Yau threefolds is encoded in the Gromov-Witten invariants.

F-Theory with Quantized Fluxes

We present evidence that the CHL string in eight dimensions is dual to F-theory compactified on an elliptic K3 with a $\Gamma_{0}(2)$ monodromy group. The monodromy group $\Gamma_{0}(2)$ allows one to turn on the flux of an antisymmetric two form along the base. The $B_{\mu \nu}$ flux is quantized and therefore the moduli space of the CHL string is disconnected from the moduli space of F-theory/Heterotic strings (as expected). The non-zero $B_{\mu \nu}$ flux obstructs certain deformations restricting the moduli of elliptic K3 to a 10 dimensional moduli space. We also discuss how one can reconstruct the gauge groups from the elliptic fibration structure.

New Type IIB Vacua and their F-Theory Interpretation

We discuss a D3-D7 system in type IIB string theory. The near-horizon geometry is described by AdS^5 x X^5 where X^5 is a U(1) bundle over a Kahler-Einstein complex surface S with positive first Chern class c_1>0. The surface S can either be P^1 x P^1, P^2 or P_{n_1,...,n_k}, a blow up of P^2 at k points with 3\leq k\leq 8. The P^2 corresponds to the maximally supersymmetric AdS^5 x S^5 vacuum while the other cases lead to vacua with less supersymmetries. In the F-theory context they can be viewed as compactifications on elliptically fibered almost Fano 3-folds.

The Large N Limit of ${\cal N} =2,1$ Field Theories from Threebranes in F-theory

We consider field theories arising from a large number of D3-branes near singularities in F-theory. We study the theories at various conformal points, and compute, using their conjectured string theory duals, their large $N$ spectrum of chiral primary operators. This includes, as expected, operators of fractional conformal dimensions for the theory at Argyres-Douglas points. Additional operators, which are charged under the (sometimes exceptional) global symmetries of these theories, come from the 7-branes. In the case of a $D_4$ singularity we compare our results with field theory and find agreement for large $N$. Finally, we consider deformations away from the conformal points, which involve finding new supergravity solutions for the geometry produced by the 3-branes in the 7-brane background. We also discuss 3-branes in a general background.

N=1 Heterotic/F-Theory Duality

We review aspects of N=1 duality between the heterotic string and F-theory. After a description of string duality intended for the non-specialist the framework and the constraints for heterotic/F-theory compactifications are presented. The computations of the necessary Calabi-Yau manifold and vector bundle data, involving characteristic classes and bundle moduli, are given in detail. The matching of the spectrum of chiral multiplets and of the number of heterotic five-branes respectively F-theory three-branes, needed for anomaly cancellation in four-dimensional vacua, is pointed out. Several examples of four-dimensional dual pairs are constructed where on both sides the geometry of the involved manifolds relies on del Pezzo surfaces.

An SL(2, Z) anomaly in IIB supergravity and its F-theory interpretation

The SL(2,IZ) duality transformations of type IIB supergravity are shown to be anomalous in generic F-theory backgrounds due to the anomalous transformation of the phase of the chiral fermion determinant. This gives a topological restriction on consistent backgrounds of the euclidean theory. A similar, but slightly stronger, restriction is also derived from an explicit F-theory compactification on K3 X M8 (where M8 is an eight-manifold with a nowhere vanishing chiral spinor) where the cancellation of tadpoles for Ramond--Ramond fields is only possible if M8 has an Euler character that is a positive multiple of 24. The interpretation of this restriction in the dual heterotic theory on T2 X M8 is also given.

Massive String Theories From M-Theory and F-Theory

The massive IIA string theory whose low energy limit is the massive supergravity theory constructed by Romans is obtained from M-theory compactified on a 2-torus bundle over a circle in a limit in which the volume of the bundle shrinks to zero. The massive string theories in 9-dimensions given by Scherk-Schwarz reduction of IIB string theory are interpreted as F-theory compactified on 2-torus bundles over a circle. The M-theory solution that gives rise to the D8-brane of the massive IIA theory is identified.

[1]High Energy Physics - Theory, abstract hep-th/9602022 From: Cumrun Vafa <vafa@string.harvard.edu> Date: Mon, 5 Feb 96 15:42:02 -0500  (14kb)  Authors: Cumrun Vafa Comments: 18 pages  Report-no: HUTP-96/A004 Journal-ref: Nucl.Phys. B469 (1996) 403-418

[2] High Energy Physics - Theory, abstract hep-th/9702173 From: Yaron Oz <yaronoz@theorm.lbl.gov> Date: Mon, 24 Feb 1997 23:24:19 MST   (17kb) Date (revised): Tue, 25 Feb 1997 20:31:12 MST Authors: Kentaro Hori, Yaron Oz   Comments: 13 pages, latex Report-no: LBNL 40031   Journal-ref: Nucl.Phys. B501 (1997) 97-108

[3]High Energy Physics - Theory, abstract hep-th/9703012 Authors: N. Khviengia, Z. Khviengia, H. Lu, C.N. Pope  From: pope@phys.tamu.edu Date: Sun, 02 Mar 1997 12:17:45 CST (19kb)Date (revised): Sat, 08 Mar 1997 17:16:42 CST Report-no: CTP-TAMU-13/97, LPTENS-97/07 Journal-ref: Class.Quant.Grav. 15 (1998) 759-773

[4]High Energy Physics - Theory, abstract hep-th/9703070

From: Masako Asano <asano@hep1.c.u-tokyo.ac.jp> Date: Mon, 10 Mar 97 13:53:17 +0900 (12kb) Author: Masako Asano Comments: 17 pages, Latex

Report-no: UT-Komaba/97-6 Journal-ref: Nucl.Phys. B503 (1997) 177-192

[5]High Energy Physics - Theory, abstract hep-th/9704009 From: Jose M Figueroa-O'Farrill <j.m.figueroa@qmw.ac.uk> Date: Tue, 1 Apr 1997 16:56:18 MST   (11kb)

Authors: JM Figueroa-O'Farrill Comments: 11 pages Report-no: QMW-PH-97-11

[6]High Energy Physics - Theory, abstract hep-th/9706155 From: "Clifford V. Johnson" <cvj@pa.uky.edu> Date: Mon, 23 Jun 1997 04:39:39 -0400   (22kb) Date (revised): Sun, 29 Jun 1997 18:21:10 -0400 Author: Clifford V. Johnson Comments: 20 pages, harvmac.tex (b), epsf.tex for decoration (Two references added. Fixed a few comments.) Report-no: UK/97-13 Journal-ref: Nucl.Phys. B507 (1997) 227-244

[7]High Energy Physics - Theory, abstract  hep-th/9707014 From: Paul S. Aspinwall <psa@physics.rutgers.edu> Date: Tue, 1 Jul 1997 09:49:56 MDT  (24kb) Date (revised): Mon, 21 Jul 1997 09:00:59 MDT Authors: Paul S. Aspinwall Comments: 19 pages, 5 figues, references added

Report-no: RU-97-55 Journal-ref: Adv.Theor.Math.Phys. 1 (1998) 127-147

[8]High Energy Physics - Theory, abstract hep-th/9709159 From: Ashoke sen <sen@mri.ernet.in> Date: Sun, 21 Sep 1997 13:05:22 GMT(12kb) Author: Ashoke Sen Comments: LaTeX file, 14 pages, 3 figures, Talk at STRINGS'97 and Trieste conference on Duality Symmetries Report-no: MRI-PHI/97/P970924 Journal-ref: Nucl.Phys.Proc.Suppl. 68 (1998) 92-98; Nucl.Phys.Proc.Suppl. 67 (1998) 81-87

[9] High Energy Physics - Theory, abstract  hep-th/9712017 From: Stephen F. Hewson <s.f.hewson@damtp.cam.ac.uk> Date: Mon, 1 Dec 1997 16:08:41 GMT   (18kb)  Authors: S. F. Hewson  Comments: 20 pages, no figures, latex  Report-no: DAMTP-R-97-58

[10]High Energy Physics - Theory, abstract hep-th/9712023 From: Calin Iuliu Lazaroiu <lazaroiu@cuphy3.phys.columbia.edu> Date (v1): Tue, 2 Dec 1997 21:52:34 GMT   (45kb)

Date (revised v2): Thu, 14 May 1998 18:46:06 GMT (45kb) Authors: M. Bershadsky, T. M. Chiang, B. R. Greene, A. Johansen, C. I. Lazaroiu Comments: 40 pages, no figures; minor cosmetic reorganization of section 4; reference [6] updated Report-no: CU-TP-870, HUTP/97-A050, CLNS 97/1524  Journal-ref: Nucl.Phys. B527 (1998) 531-570

[11]High Energy Physics - Theory, abstract hep-th/9801111 Authors: S. Penati, A. Santambrogio, D. Zanon From: Alberto.Santambrogio@mi.infn.it Date:Fri, 16 Jan 1998 12:42:09 GMT (9kb) Comments: 9 pages, latex, no figures, to appear in the proceedings of "Quantum Aspects of Gauge Theories, Supersymmetry and Unification" Neuchatel, September 18-23, 1997 Report-no: IFUM-595-FT

[12]High Energy Physics - Theory, abstract hep-th/9802093 Authors: Ron Y. Donagi

From: donagi@math.upenn.edu  Date: Thu, 12 Feb 1998 22:57:17 GMT (11kb)

Comments: 9 pages, Latex Subj-class: High Energy Physics - Theory; Algebraic Geometry

[13]High Energy Physics - Theory, abstract hep-th/9803168 From: Per Berglund <berglund@itp.ucsb.edu> Date (v1): Fri, 20 Mar 1998 00:59:31 GMT (43kb) Date (revised v2): Tue, 28 Apr 1998 18:02:03 GMT (43kb) Authors: P. Berglund, E. G. Gimon Comments: 36 pages, 4 eps figures, use harvmac and epsf. Typos corrected Report-no: CALT-68-2164, NSF-ITP-98-025 Journal-ref: Nucl.Phys. B525 (1998) 73-103

[14]High Energy Physics - Theory, abstract hep-th/9803241 From: International Department <interdep@kinr.kiev.ua> Date: Mon, 30 Mar 1998 09:54:44 GMT (3kb) Authors: Yu. Malyuta, T. Obikhod Comments: 7 pages, LATEX

[15]High Energy Physics - Theory, abstract hep-th/9804092 From: Zurab Kakushadze <zurab@string.harvard.edu> Date (v1): Mon, 13 Apr 1998 23:20:26 GMT  (63kb) Date (revised v2): Sat, 9 May 1998 07:20:24 GMT (63kb) Authors: Zurab Kakushadze, Gary Shiu, S.-H. Henry Tye Comments: 62 pages, revtex, 2 figures, minor misprints corrected, references and acknowledgments added

[16] High Energy Physics - Theory, abstract hep-th/9804178 From: International Department <interdep@kinr.kiev.ua> Date: Tue, 28 Apr 1998 09:14:43 GMT (3kb) Authors: Yu. Malyuta, T. Obikhod Comments: 7 pages, LATEX

[17] High Energy Physics - Theory, abstract hep-th/9805056 From: Michael Bershadsky <bershad@string.harvard.edu> Date (v1): Mon, 11 May 1998 14:01:02 GMT  (72kb) Date (revised v2): Thu, 28 May 1998 17:36:59 GMT   (73kb) Authors: Michael Bershadsky, Tony Pantev, Vladimir Sadov Comments: 41 pages, harvmac, 35 figures, references corrected  Report-no: HUTP-98/A029

[18]High Energy Physics - Theory, abstract hep-th/9805131 From: Alexandros Kechagias <Alexandros.Kehagias@cern.ch> Date: Wed, 20 May 1998 23:54:41 GMT   (12kb)

Authors: A. Kehagias  Comments: 12 pages, latex  Report-no: CERN-TH/98157

Journal-ref: Phys.Lett. B435 (1998) 337-342

[19]High Energy Physics - Theory, abstract hep-th/9806159

From: Juan Maldacena <malda@bose.harvard.edu> Date (v1): Thu, 18 Jun 1998 23:05:06 GMT   (26kb) Date (revised v2): Fri, 19 Jun 1998 00:18:46 GMT   (26kb)  Date (revised v3): Sat, 20 Jun 1998 18:03:53 GMT   (26kb) Authors: Ofer Aharony, Ansar Fayyazuddin, Juan Maldacena

Report-no: HUTP-98/A046, RU-98-26 Journal-ref: J.High Energy Phys. 07 (1998) 013

[20]High Energy Physics - Theory, abstract hep-th/9808159

From: Bjoern Andreas <andreas@physik.hu-berlin.de>

Date: Wed, 26 Aug 1998 13:43:47 GMT (58kb) Author: Bjorn Andreas Comments: 82pp,latex

[21]High Energy Physics - Theory, abstract hep-th/9810153

From: M B Green <M.B.Green@damtp.cam.ac.uk> Date (v1): Tue, 20 Oct 1998 20:46:05 GMT (19kb) Date (revised v2): Fri, 30 Oct 1998 13:27:27 GMT (20kb)

Authors: Matthias R. Gaberdiel, Michael B. Green Comments: References added and minor stylistic changes. 21 pages, harvmac (b) Report-no: DAMTP-98-102

[22]High Energy Physics - Theory, abstract hep-th/9811021

From: Chris Hull <C.M.Hull@qmw.ac.uk> Date: Mon, 2 Nov 1998 19:07:39 GMT (11kb) Authors: C.M. Hull Comments: 15 Pages, Tex, Phyzzx Macro Report-no: QMW-PH-98-36, LPTENS 98/32